{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"5be307c1ade7c6effe2c96d69c5846ae4ba5371e69b46800120348aa3f6e5c72","created":"2026-10-03T07:18:08Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"f49c7852d3d1b172e4e2f3fe0e0dabd1785aa9270e79983a5c4a49ca8c5b8b42","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"qft.cft-rg.qed3-critical-nf","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"Electrodynamics in two space dimensions with N species of massless electrons is scale invariant at long distances when N is large. Below which N this fails is unknown.","posed_since":"","precise":"3D QED with $N_{f}$ two-component Dirac fermions of unit charge ($N_{f}$ even, parity invariant) flows to an interacting CFT for large $N_{f}$. Determine $N_{f}^{c}$ such that for $N_{f} < N_{f}^{c}$ the IR breaks the $\\mathrm{SU}(N_{f})$ flavor symmetry or is otherwise not conformal; in particular decide $N_{f} = 2$ and $N_{f} = 4$ (the latter describes the Dirac spin liquid).","problem_ref":null,"references":"","settled_by":"Conformal bootstrap islands or continuum-extrapolated lattice simulations that bracket $N_{f}^{c}$ and determine the fate of $N_{f}=2\\text{ and }4$.","status_note":"Estimates from Schwinger-Dyson equations, $\\epsilon$ expansion, the F-theorem, lattice simulations and bootstrap disagree; recent lattice and bootstrap evidence favors conformality at $N_f = 4$.","title":"Critical flavor number for chiral symmetry breaking in QED3","topic_ref":"59b3cca1f32dc01e525b6517c866b60ced9512aa01bc51694ea2f6fc00c1ca06"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"ab9d673db327eb13ea4e7e2c0a832e1350a09c4a9e87ca2c45adfca777a874c7","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"905b87d6918471b1fad67ae99368baf92338d93f0cfbd6b0cb09a2c6c47d31cb","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"1XOmJKYhoyjROXJ3xUww-SKr58PrWwgZzBQei6162hkEWB41avmHXtxg0Pa4HIu9kHnR4SMIgplwt6jqt6MWBA"},"schema":"pubphys.envelope/1"},"record_hash":"ab9d673db327eb13ea4e7e2c0a832e1350a09c4a9e87ca2c45adfca777a874c7","leaf_index":1895}